deepxde.nn.tensorflow_compat_v1

deepxde.nn.tensorflow_compat_v1.deeponet module

class deepxde.nn.tensorflow_compat_v1.deeponet.DeepONet(layer_sizes_branch, layer_sizes_trunk, activation, kernel_initializer, regularization=None, use_bias=True, stacked=False, trainable_branch=True, trainable_trunk=True)

Bases: deepxde.nn.tensorflow_compat_v1.nn.NN

Deep operator network.

Lu et al. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intell, 2021.

Parameters:

• layer_sizes_branch – A list of integers as the width of a fully connected network, or (dim, f) where dim is the input dimension and f is a network function. The width of the last layer in the branch and trunk net should be equal.
• layer_sizes_trunk (list) – A list of integers as the width of a fully connected network.
• activation – If activation is a string, then the same activation is used in both trunk and branch nets. If activation is a dict, then the trunk net uses the activation activation[“trunk”], and the branch net uses activation[“branch”].
• trainable_branch – Boolean.
• trainable_trunk – Boolean or a list of booleans.

build()

Construct the network.

inputs

Return the net inputs (placeholders).

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).

class deepxde.nn.tensorflow_compat_v1.deeponet.DeepONetCartesianProd(layer_size_branch, layer_size_trunk, activation, kernel_initializer, regularization=None)

Bases: deepxde.nn.tensorflow_compat_v1.nn.NN

Deep operator network for dataset in the format of Cartesian product.

Parameters:

• layer_size_branch – A list of integers as the width of a fully connected network, or (dim, f) where dim is the input dimension and f is a network function. The width of the last layer in the branch and trunk net should be equal.
• layer_size_trunk (list) – A list of integers as the width of a fully connected network.
• activation – If activation is a string, then the same activation is used in both trunk and branch nets. If activation is a dict, then the trunk net uses the activation activation[“trunk”], and the branch net uses activation[“branch”].

build()

Construct the network.

inputs

Return the net inputs (placeholders).

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).

deepxde.nn.tensorflow_compat_v1.fnn module

class deepxde.nn.tensorflow_compat_v1.fnn.FNN(layer_sizes, activation, kernel_initializer, regularization=None, dropout_rate=0, batch_normalization=None, layer_normalization=None, kernel_constraint=None, use_bias=True)

Bases: deepxde.nn.tensorflow_compat_v1.nn.NN

Fully-connected neural network.

build()

Construct the network.

inputs

Return the net inputs (placeholders).

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).

class deepxde.nn.tensorflow_compat_v1.fnn.PFNN(layer_sizes, activation, kernel_initializer, regularization=None, dropout_rate=0, batch_normalization=None)

Bases: deepxde.nn.tensorflow_compat_v1.fnn.FNN

Parallel fully-connected neural network that uses independent sub-networks for each network output.

Parameters:layer_sizes – A nested list to define the architecture of the neural network (how the layers are connected). If layer_sizes[i] is int, it represent one layer shared by all the outputs; if layer_sizes[i] is list, it represent len(layer_sizes[i]) sub-layers, each of which exclusively used by one output. Note that len(layer_sizes[i]) should equal to the number of outputs. Every number specify the number of neurons of that layer.

build()

Construct the network.

deepxde.nn.tensorflow_compat_v1.mfnn module

class deepxde.nn.tensorflow_compat_v1.mfnn.MfNN(layer_sizes_low_fidelity, layer_sizes_high_fidelity, activation, kernel_initializer, regularization=None, residue=False, trainable_low_fidelity=True, trainable_high_fidelity=True)

Bases: deepxde.nn.tensorflow_compat_v1.nn.NN

Multifidelity neural networks.

build()

Construct the network.

inputs

Return the net inputs (placeholders).

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).

deepxde.nn.tensorflow_compat_v1.mionet module

class deepxde.nn.tensorflow_compat_v1.mionet.MIONet(layer_sizes_branch1, layer_sizes_branch2, layer_sizes_trunk, activation, kernel_initializer, regularization=None)

Bases: deepxde.nn.tensorflow_compat_v1.nn.NN

Multiple-input operator network with two input functions.

build()

Construct the network.

inputs

Return the net inputs (placeholders).

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).

class deepxde.nn.tensorflow_compat_v1.mionet.MIONetCartesianProd(layer_sizes_branch1, layer_sizes_branch2, layer_sizes_trunk, activation, kernel_initializer, regularization=None)

Bases: deepxde.nn.tensorflow_compat_v1.mionet.MIONet

MIONet with two input functions for Cartesian product format.

build()

Construct the network.

deepxde.nn.tensorflow_compat_v1.msffn module

class deepxde.nn.tensorflow_compat_v1.msffn.MsFFN(layer_sizes, activation, kernel_initializer, sigmas, regularization=None, dropout_rate=0, batch_normalization=None, layer_normalization=None, kernel_constraint=None, use_bias=True)

Bases: deepxde.nn.tensorflow_compat_v1.fnn.FNN

Multi-scale fourier feature networks.

Parameters:sigmas – List of standard deviation of the distribution of fourier feature embeddings.

References

S. Wang, H. Wang, & P. Perdikaris. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 384, 113938, 2021.

build()

Construct the network.

class deepxde.nn.tensorflow_compat_v1.msffn.STMsFFN(layer_sizes, activation, kernel_initializer, sigmas_x, sigmas_t, regularization=None, dropout_rate=0, batch_normalization=None, layer_normalization=None, kernel_constraint=None, use_bias=True)

Bases: deepxde.nn.tensorflow_compat_v1.msffn.MsFFN

Spatio-temporal multi-scale fourier feature networks.

References

S. Wang, H. Wang, & P. Perdikaris. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 384, 113938, 2021.

build()

Construct the network.

deepxde.nn.tensorflow_compat_v1.nn module

class deepxde.nn.tensorflow_compat_v1.nn.NN

Bases: object

Base class for all neural network modules.

apply_feature_transform(transform)

Compute the features by appling a transform to the network inputs, i.e., features = transform(inputs). Then, outputs = network(features).

apply_output_transform(transform)

Apply a transform to the network outputs, i.e., outputs = transform(inputs, outputs).

auxiliary_vars

Return additional variables needed (placeholders).

build()

Construct the network.

built

feed_dict(training, inputs, targets=None, auxiliary_vars=None)

Construct a feed_dict to feed values to TensorFlow placeholders.

inputs

Return the net inputs (placeholders).

num_trainable_parameters()

Evaluate the number of trainable parameters for the NN.

Notice that the function returns the number of trainable parameters for the whole tf.Session, so that it will not be correct if several nets are defined within the same tf.Session.

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).

deepxde.nn.tensorflow_compat_v1.resnet module

class deepxde.nn.tensorflow_compat_v1.resnet.ResNet(input_size, output_size, num_neurons, num_blocks, activation, kernel_initializer, regularization=None)

Bases: deepxde.nn.tensorflow_compat_v1.nn.NN

Residual neural network.

build()

Construct the network.

inputs

Return the net inputs (placeholders).

outputs

Return the net outputs (tf.Tensor).

targets

Return the targets of the net outputs (placeholders).